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Connecting spatial and temporal scales of tropical precipitation in observations and the MetUMGA6 Article

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Martin, G. M., Klingaman, N. P. and Moise, A. F. (2017) Connecting spatial and temporal scales of tropical precipitation in observations and the MetUMGA6. Geoscientific Model Development, 10 (1). pp. 105126. ISSN 19919603 doi: https://doi.org/10.5194/gmd101052017 Available at http://centaur.reading.ac.uk/68444/

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Geosci. Model Dev., 10, 105–126, 2017www.geosci-model-dev.net/10/105/2017/doi:10.5194/gmd-10-105-2017© Author(s) 2017. CC Attribution 3.0 License.

Connecting spatial and temporal scales of tropical precipitation inobservations and the MetUM-GA6Gill M. Martin1, Nicholas P. Klingaman2, and Aurel F. Moise3

1Met Office, Exeter, UK2National Centre for Atmospheric Science-Climate and Department of Meteorology, University of Reading, UK3Bureau of Meteorology, Melbourne, Australia

Correspondence to: Gill M. Martin ([email protected])

Received: 28 July 2016 – Published in Geosci. Model Dev. Discuss.: 13 September 2016Revised: 1 December 2016 – Accepted: 13 December 2016 – Published: 6 January 2017

Abstract. This study analyses tropical rainfall variability (ona range of temporal and spatial scales) in a set of parallel MetOffice Unified Model (MetUM) simulations at a range of hor-izontal resolutions, which are compared with two satellite-derived rainfall datasets. We focus on the shorter scales, i.e.from the native grid and time step of the model through sub-daily to seasonal, since previous studies have paid relativelylittle attention to sub-daily rainfall variability and how thisfeeds through to longer scales. We find that the behaviour ofthe deep convection parametrization in this model on the na-tive grid and time step is largely independent of the grid-boxsize and time step length over which it operates. There is alsolittle difference in the rainfall variability on larger/longer spa-tial/temporal scales. Tropical convection in the model on thenative grid/time step is spatially and temporally intermittent,producing very large rainfall amounts interspersed with gridboxes/time steps of little or no rain. In contrast, switching offthe deep convection parametrization, albeit at an unrealisticresolution for resolving tropical convection, results in verypersistent (for limited periods), but very sporadic, rainfall. Inboth cases, spatial and temporal averaging smoothes out thisintermittency. On the ∼100 km scale, for oceanic regions,the spectra of 3-hourly and daily mean rainfall in the config-urations with parametrized convection agree fairly well withthose from satellite-derived rainfall estimates, while at ∼10-day timescales the averages are overestimated, indicating alack of intra-seasonal variability. Over tropical land the re-sults are more varied, but the model often underestimates thedaily mean rainfall (partly as a result of a poor diurnal cycle)but still lacks variability on intra-seasonal timescales. Ulti-mately, such work will shed light on how uncertainties in

modelling small-/short-scale processes relate to uncertaintyin climate change projections of rainfall distribution and vari-ability, with a view to reducing such uncertainty through im-proved modelling of small-/short-scale processes.

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1 Introduction

The realism of rainfall in a climate model is a key indicatorof its skill in representing the underlying physical processes,and hence in increasing our confidence for projecting futurechanges in rainfall. In particular, the spatial and temporalstructure of rainfall variability is arguably a more importantindicator of this skill than the absolute rainfall amount or theaggregated mean state, which is typically used to assess mod-els. When and where rainfall will occur, and with what in-tensity and duration, is essential information, particularly invulnerable tropical regions where the livelihoods of millionsrely on seasonal, rainfall-driven agriculture and where in-frastructure is often lacking, even when extremes associated

Published by Copernicus Publications on behalf of the European Geosciences Union.

106 G. M. Martin et al.: Connecting spatial and temporal scales of tropical precipitation

with rainfall variability (droughts, floods) are relatively com-monplace. Although there have been some improvements insome aspects of the representation of precipitation betweenthe 3rd and 5th phases of the Climate Model Intercompar-ison Project (CMIP3, Meehl et al., 2007, and CMIP5, Tay-lor et al., 2012, respectively), as described, for example, inKoutroulis et al. (2016), uncertainties in hydrological predic-tions from the current generation of models still pose a seri-ous challenge to the reliability of projections across temporaland spatial scales (Trenberth, 2011).

Previous studies have highlighted that climate model bi-ases on multi-year and global scales develop within a fewdays of the start of the simulation (e.g. Martin et al., 2010)and are closely related to deficiencies in the simulation ofprocesses on much shorter and smaller scales (e.g. Stephenset al., 2010). Such mean state biases in rainfall can be asso-ciated with other biases such as in sea surface temperatures(e.g. Levine and Turner, 2012) and can contribute to uncer-tainty in projections of future tropical rainfall (e.g. Kent etal., 2015). Deep convection parametrizations in these mod-els often produce very intermittent rainfall at the level of themodel’s time step and gridscale, and also produce a poor rep-resentation of the processes and timing associated with thediurnal cycle of convection over land (e.g. Stratton and Stir-ling, 2012). Such deficiencies can have a significant impacton the regional-scale circulation and water cycle (e.g. Birchet al., 2014). Studies such as Kendon et al. (2014) illustratedthat representing rainfall characteristics on short and smallscales may be paramount in order to eliminate these biasesand thereby provide confidence in projections of the spatialand temporal characteristics of heavy rainfall in a future cli-mate.

The sheer volume of data required for analyses of rainfallvariability at sub-daily timescales and kilometre-scale res-olutions can deter model developers. Analysis of sub-dailyrainfall variability is therefore relatively limited in the scien-tific literature. However, the importance of studying changesin the location, type, amount, frequency, intensity and dura-tion of precipitation, and especially to changes in extremes,has been highlighted by several authors in recent years (e.g.Trenberth, 2011; Tripathi and Dominguez, 2013; Cortez-Hernandez et al., 2015). Studies of sub-daily rainfall and ex-tremes in observations (e.g. Westra et al., 2014) and in mod-els (e.g. Rosa and Collins, 2013) are becoming more com-mon in the literature and highlight discrepancies betweenmodels and observations and sensitivities to model resolu-tion and physical parametrizations.

Klingaman et al. (2017) showed how these large datavolumes can be condensed to a manageable set of di-agnostics (Analysing Scales of Precipitation Version 1.0,ASoP1) with which we can both increase understanding ofobserved rainfall variability and compare model behaviouron a range of timescales and space scales. The ASoP di-agnostics include correlations with distance and time, aswell as one-dimensional (1-D) and 2-D spectra of rainfall

amounts, and can be applied to data on any timescale or spacescale, although the diagnostics are designed for the range oftime step/gridscale up to sub-seasonal/meso-α scale (∼90days/∼500 km). Klingaman et al. (2017) applied ASoP1 toIndo-Pacific Warm Pool precipitation data from 10 mod-els used in the “Vertical structure and physical processesof the Madden–Julian Oscillation” model-evaluation project(Xavier et al., 2015). The authors found large inter-modelvariations in the degree of spatial and temporal intermittencyin time step precipitation, but that the models’ scales of pre-cipitation were highly similar when the precipitation datawere averaged to the 3 h, 600 km scale.

Motivated by those results, in the present study we usethe ASoP1 methods to examine how the spatial and tempo-ral intermittency of tropical precipitation in the Met Officeglobal general circulation model (GCM) varies with horizon-tal resolution – and, by extension, time step length – and thetreatment of deep convection. In Klingaman et al. (2017), theMet Office Unified Model (MetUM) displayed particularlyhigh spatial and temporal intermittency in time step and grid-scale precipitation. Here, we analyse sub-daily precipitationintermittency in the simulations across a range of horizontalresolutions with parametrized convection, as well as in a sim-ulation with an explicit representation of mid-level and deepconvection. In all cases, we examine how sub-daily precipi-tation intermittency may influence rainfall characteristics atlonger timescales (up to ∼20 days), in order to demonstratehow the ASoP1 diagnostics can be used routinely as part ofmodel parametrization development.

The paper is arranged as follows. In Sect. 2 we provide de-tails of the model and observation datasets used in this study,in Sect. 3 we analyse the temporal and spatial coherence ofthe tropical rainfall on sub-daily timescales, in Sect. 4 we ex-amine the spectral distributions of rainfall amounts at a rangeof timescales and space scales up to ∼20 days and our dis-cussion and conclusions are presented in Sect. 5.

2 Datasets used in this study

2.1 Model description

We use the MetUM Global Atmosphere version 6.0(MetUM-GA6; Walters et al., 2016; Williams et al., 2015),which is an updated version of the MetUM-GA3 (Walters etal., 2011) configuration analysed by Klingaman et al. (2017),with a different dynamical core (ENDGAME; Wood et al.,2014 orographic gravity-wave drag representation (Vosper etal., 2009), and several changes to the convective parametriza-tion (see Walters et al. (2011, 2016) for details). MetUM-GA6 includes a 25 % increase to the rates of mixing entrain-ment and detrainment for diagnosed deep convection relativeto MetUM-GA3, implemented to improve the representationof tropical sub-seasonal variability following Klingaman andWoolnough (2014). MetUM-GA6 atmosphere-only simula-

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G. M. Martin et al.: Connecting spatial and temporal scales of tropical precipitation 107

Table 1. For each MetUM-GA6.0 simulation: the name of the simulation, the horizontal resolution in degrees (to the nearest 0.01◦) andthe equivalent in kilometres at the Equator, the time step, the largest domain over which data were extracted, the representation of deepconvection (either a sub-gridscale parametrization or entirely “explicit” convection) and the years of daily (time step) data analysed. Notethat data are limited to June, July, August, and September of any given year. Models are listed in order of decreasing horizontal grid spacing,as in the figures.

Name Long◦ × lat◦

(km)Timestepmin-utes

Available datadomain

Deepconvection

Years analysedfor daily (timestep) data

N96 1.88◦× 1.25◦

(210× 139)20 20◦ S–40◦ N,

20◦W–160◦ Eparametrized 1982–2008

(1990)

N216 0.83◦× 0.56◦

(92× 62)15 20◦ S–40◦ N,


(1990)

N512 0.35◦× 0.23◦

(39× 26)10 20◦ S–40◦ N,


(2007)

N1024p 0.18◦× 0.12◦

(20× 13)5 0–20◦ N,

130–160◦ Eparametrized (2005)

N1024p 0.18◦× 0.12◦

(20× 13)5 8–17◦ N,

0–10◦ Eparametrized (2005)

N1024e 0.18◦× 0.12◦

(20× 13)5 0–20◦ N,

130–160◦ Eexplicit (2005)

N1024e 0.18◦× 0.12◦

(20× 13)5 8–17◦ N,

0–10◦ Eexplicit (2005)

tions are forced with daily observed sea surface temperature(SST) and sea ice forcings from the OSTIA product (Donlonet al., 2012), bilinearly interpolated from the OSTIA 1/20◦

resolution to the MetUM horizontal grids.The MetUM-GA6 naming conventions and parameter set-

tings for the different resolutions used in the current studymatch those described by Johnson et al. (2016) for MetUM-GA3. As discussed by Johnson et al. (2016), very few param-eters in the MetUM are changed with resolution, but thereare a few that must be changed to ensure numerical stability.In the MetUM-GA6 simulations analysed in our study, mostof the parameter settings for the different resolutions matchthose shown in Johnson et al. (2016; their Table 2). Note thatthe inclusion of the ENDGAME dynamical core improvedmodel stability, negating the need for targeted diffusion ofmoisture. An additional resolution, termed “N1024”, with a0.18◦× 0.12◦ grid, is also included. The settings at N1024resolution are also kept the same, except for the dynamicalcore’s alternating-direction implicit (ADI) pseudo-time step,which is related to the efficiency of the implicit solver at highlatitudes. This is reduced to 7× 10−5 in the N1024 simula-tions.

Table 1 contains details of the MetUM-GA6 simulationsand the domains over which we analyse the precipitationdata. Time step rainfall data for an extended tropical region(40◦ S–40◦ N) were archived for only one June–September

season (JJAS) due to their computational and storage costs.The year of output depended on when the time step diag-nostics were enabled manually; for the N512 simulation thiswas originally 1985. However, due to a technical error in theoriginal diagnostic output, the simulation had to be repeated,using the same configuration and with time step diagnosticsenabled, for June–September 2007, due to the availability ofa 1 June restart file for that year. Daily data were availablefor at least 8 years (often 27 years), from 1982 onwards, inall but the N1024 simulations, which were run for only 4years due to computational cost. Due to the relatively smallamount of daily data available for the N1024 simulations,only the time step data for these configurations are includedin this study. Despite time step data being available for dif-fering years between the runs, we consider that the sampleis sufficiently large for the results to be robust. Comparisonof other model runs (not shown) where more than one sea-son of time step data was available have also shown that theresults have little sensitivity to the year used. In the anal-ysis of spatial and temporal intermittency, for most of thesimulations we analyse a tropical domain covering the equa-torial Indian Ocean, Maritime Continent and the far west-ern Pacific Ocean (10◦ S–10◦ N, 60–160◦ E), hereafter the“EQ” domain. For the spectral analyses we use a larger do-main covering 20◦ S–40◦ N, 20◦W–160◦ E. For the highestresolution (N1024) simulations, we use data only over the

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Table 2. For each MetUM-GA6 resolution, as well as TRMM and CMORPH: the analysis region used; the dimensions of each region innative grid boxes; the number of model time steps in 3 h; the number of native grid boxes in an N48 grid box (rounded to the nearest wholegrid box); the number of 7× 7 native grid box regions in the analysis domain; and the number of “equal-area” 1700 and 600 km regions inthe analysis domain, with the dimensions of the regions (in native grid boxes) shown in parentheses.

Dataset Region Size 1t No. of boxes No. of 7 × No. of 1700 km No. of 600 km(nx × ny) in 3 h in N48 7 regions regions (nx × ny) regions (nx × ny)

N96 EQ 53 × 16 9 4 14 6 (8 × 12) n/aN216 EQ 120 × 36 12 20 85 6 (18 × 27) n/aN512 EQ 284 × 86 18 113 480 6 (43 × 64) n/aN512 WP 85 × 85 18 113 144 n/a 15 (15 × 23)N1024p WP 170 × 171 36 455 576 n/a 15 (30 × 46)N1024e WP 170 × 171 36 455 576 n/a 15 (30 × 46)N48 averaged EQ 28 × 9 n/a 1 4 6 (4 × 6) n/aN48 averaged WP 9 × 9 n/a 1 1 2 (4 × 6) n/aTRMM EQ 400 × 80 1 150 627 6 (51 × 51) n/aCMORPH EQ 400 × 80 1 150 627 6 (51 × 51) n/aCMORPH WP 1 150 187 n/a 15 (22 × 22)

two limited domains that were available to us (due to stor-age and computational limits), one in the western PacificOcean (0–20◦ N, 130–160◦ E; hereafter the “WP” domain),and the other over western Africa (8–17◦ N, 0–10◦ E, here-after the “WA” domain). We use data from the next-finestresolution (N512) to demonstrate that there are limited dif-ferences in sub-daily precipitation characteristics over oceanbetween the EQ and WP domains. The domains used are il-lustrated in Fig. 1.

As an additional test of the ability of the ASoP1 diagnos-tics to identify different behaviour in rainfall variability, wealso analyse a N1024 simulation where parametrized deepconvection is switched off (N1024e). Although this simula-tion has a horizontal resolution at which explicit convectionis unlikely to be realistic, it is worth exploiting the oppor-tunity afforded by this pair of simulations to compare therainfall variability with and without parametrized deep con-vection, but at the same horizontal resolution and model timestep.

2.2 Satellite-based rainfall analyses

We compare the models’ precipitation data with two sets ofsatellite-derived analyses: those from the Tropical RainfallMeasuring Mission 3B42 product, version 7 (TRMM; Kum-merow et al., 1998a; Huffman et al., 2007, 2010) and thosefrom the CPC MORPHing technique version 1.0 (CMORPH;Joyce et al., 2004). Both products are derived from a com-bination of infrared and microwave sounders and calibratedagainst gauge data. TRMM and CMORPH are available at3-hourly and daily time resolution and a maximum horizon-tal resolution of 0.25◦× 0.25◦. We analyse daily averagesof these products across a common period of 2001–2012,while JJAS from the year 2005 is used for analysis of theraw 3-hourly data, for comparison against the single JJAS of

3-hourly data from each model configuration. Comparisonsof the results for 3-hourly data between this single JJAS sea-son and all JJAS seasons from each dataset show only smalldifferences (not shown), confirming that the use of a singleseason is justified.

3 Sub-daily spatial and temporal intermittency

3.1 Behaviour on the native grid and time step

2-D probability distribution functions (PDFs) of binned grid-box precipitation in a time interval t against precipitationin the next interval t + 1 are used to diagnose the be-haviour of satellite-derived and simulated precipitation be-tween consecutive temporal intervals at a fixed horizontalpoint (see Klingaman et al., 2017, for details of the method-ology). When applied to time step data on the native gridfrom MetUM-GA6 simulations with parametrized convec-tion (Fig. 2a–e), these PDFs show higher probabilities alongthe axes and lower probabilities on the central diagonal. Thisdemonstrates that, with parametrized convection, MetUM-GA6 produces substantial temporal intermittency in timestep, grid-box precipitation, as heavy precipitation on onetime step is followed by light or no precipitation on thenext time step, and vice versa. There is very little variationin this behaviour with horizontal resolution and time steplength: over the EQ domain, N512 rainfall similarly intermit-tent to N96 rainfall, despite a∼25-fold reduction in grid-boxarea; over the WP domain, N1024p rainfall is similarly inter-mittent to N512 rainfall, despite a 4-fold reduction in grid-box area. Comparing N512-EQ and N512-WP demonstratesthat temporal intermittency in rainfall is similar in these re-gions, suggesting that N1024p-WP can be compared with thecoarser-resolution models over the EQ domain.



Figure 1. Map illustrating the regions used in this study. “WA”: western Africa; “WP” western Pacific; “EQ”: equatorial region. See text forfurther details.

Perhaps most striking is the consistency of the timestep rain-rate PDFs (dashed line) among the parametrized-convection configurations, regardless of the horizontal reso-lution. Resolution hardly alters the PDF of time step rain-fall, when converted to daily rates, which indicates thatthe convective parametrization is not strongly affected bychanges in grid-box area or the associated changes in thestrength of the dynamical forcing. We hypothesize that this isdue to an “all-or-nothing” behaviour in the MetUM convec-tive parametrization; when deep convection is triggered, theparametrization often produces the maximum possible rainrate, even for relatively weak forcing. This is consistent withthe lack of moderate time step rain rates (9–30 mm day−1) atall resolutions with parametrized convection. We note thatthe rain-rate PDFs would differ with resolution if we ex-pressed the rain rates as per time step values, but this wouldnot provide a clean comparison between the simulations.

The intermittent behaviour in the tropical deep convectiverainfall is caused by the choice of closure at GA6, in whichthe mass flux amplitude is set to depend on the ConvectiveAvailable Potential Energy (CAPE) detected in the grid box,rather than the rate of atmospheric destabilization (A. Stir-ling, personal communication, 2016). The resultant heatingapplied produces an inversion at the top of the boundary layeron the next time step that the diagnosis deems too strong toallow convection to initiate. It remains in this state until theinversion has been eroded by a combination of heating in theboundary layer and large-scale ascent. Examination of timeseries of tropical rainfall from the start of each simulation(not shown) indicates that this behaviour occurs immediatelyat the start of the simulation with very little spin-up (less than1 day), regardless of grid size or time step length.

Switching from a parametrized to an explicit treat-ment of deep convection at N1024 resolution transformsMetUM-GA6 from producing highly intermittent precipita-tion (Fig. 2e) to highly persistent precipitation (Fig. 2f). Inthe 2-D PDF of time step, grid-box precipitation, N1024eproduces high values on the diagonal and low values onthe axes, reminiscent of the most persistent models anal-ysed by Klingaman et al. (2017). However, the highly bi-

modal 1-D rain-rate PDF (dashed line in Fig. 2f) shows thatN1024e exhibits even stronger “all-or-nothing” behaviourthan N1024p. On average, only 2 % of time steps precip-itate at rates ≥ 2 mm day−1, but most of those have rates≥ 180 mm day−1. This is almost certainly due to the ex-tremely strong forcing required to lift a ∼20 km × 14 kmgrid box, and confirms that N1024e is a very coarse resolu-tion at which to use an explicit representation of deep convec-tion. Future work will investigate how this behaviour changesas the resolution is increased in convection-permitting simu-lations.

ASoP1 measures precipitation coherence as a function ofthe native time step and grid by dividing the analysis regioninto 7× 7 sub-regions, computing lag correlations of eachgrid box in the region against the central grid box, then com-positing these correlations across all sub-regions (see Klinga-man et al., 2017, for details). For ease of display, the spatialcorrelations are binned by the distance away from the cen-tral grid-box, in units of the longitudinal grid spacing at theEquator (1x). Table 2 gives the number of 7×7 sub-regionsin each model and region. In MetUM-GA6, all parametrized-convection resolutions show similarly low coherence in timestep, grid-box precipitation to that found by Klingaman etal. (2017) for MetUM-GA3, with a lag-1 minimum in theauto-correlation at the central grid box that indicates a pref-erence for “on–off” convection (Fig. 3a–e). The fact that thecorrelations between surrounding grid boxes and the centralgrid box are essentially constant at all lags shows that con-vection at the surrounding grid boxes evolves independentlyof the central grid box, confirming a lack of spatial organiza-tion. Switching to an explicit representation of convection inN1024e produces temporally consistent precipitation at thecentral grid box (Fig. 3f), but does not improve the low spa-tial coherence of rainfall, which is reduced further comparedwith N1024p. This is because convective heating associatedwith explicit convection sets up significant ascent in the con-vecting column, which continues the destabilization of thecolumn, whereas adjacent columns experience descent andso convection is suppressed.



(a) N96 EQ region (b) N216 EQ region (c) N512 EQ region

(d) N512 WP region (e) N1024p WP region (f) N1024e WP region

Figure 2. For each MetUM GA6 configuration in Table 1, the filled blocks show the 2-D histogram of binned rain rates (in mm day−1)on consecutive time steps at the same grid box, aggregated over all grid boxes; the dashed line shows the 1-D histogram of binned precip-itation, using the right-hand vertical axis. Bins were chosen qualitatively such that 3-hourly TRMM analyses over the EQ region have anapproximately uniform distribution for rain rates greater than 1 mm day−1. Note the logarithmic colour scale.

3.2 Effects of temporal averaging

To examine whether the characteristics of grid box, timestep precipitation discussed in Sect. 3.1 persist at longertimescales, we apply the 2-D histogram diagnostic fromKlingaman et al. (2017) to 3 h averaged time step precipi-tation data (Fig. 4). Such temporal averaging reduces pre-cipitation intermittency at all resolutions with parametrizedconvection, producing higher probabilities along the centraldiagonal and lower probabilities along the axes relative toFig. 2. This implies that, when averaged over 3 h, the con-vection scheme starts to display sensitivity to the large-scaleforcing, as the strength thereof determines the frequency withwhich the convection scheme can be activated. In contrast,such averaging leads to much greater intermittency for theN1024e configuration (Fig. 4i). The temporal persistenceseen in the N1024e time step data (Fig. 2f) does not carryacross to the 3-hourly scale, likely because the decorrelationtime of gridscale precipitation in the explicit-convection con-figuration is much longer than a time step (5 min) but shorterthan 6 h (i.e. two consecutive 3 h periods, as considered inthe 2-D histograms). This suggests that the grid-box precipi-tation features in N1024e, as well as the associated gridscaleforcing, often have lifetimes of 3 h or fewer.

N1024e-WP also has consecutive 3 h steps with very high(> 180 mm day−1) rainfall, which occurs about 35 % of thetime that there is rainfall in this bin (i.e. 35 % of the timethat there is > 180 mm day−1 in one 3 h window, there isalso > 180 mm day−1 in the next 3 h window). All configura-tions with parametrized convection produce 3 h rain rates thatare too persistent relative to CMORPH and TRMM, whetherthe analyses are considered on their native grids (Fig. 4a–c) or averaged to the same grids as the model configurations(shown for CMORPH only; Fig. 4j–l). Comparing CMORPHacross resolutions shows an increase in precipitation inter-mittency at finer gridscales, which MetUM-GA6 also shows,but to a more limited extent. TRMM rainfall is somewhatmore intermittent than CMORPH, but the results from allmodel configurations are outside the range of those from thesatellite-derived analyses.

3.3 Effects of spatial averaging

To test the effects of spatial averaging on the characteristicsof time step precipitation, we average the data from eachmodel to a horizontal resolution of 3.75◦× 2.5◦, which isexactly 2× 2 N96 grid boxes and equivalent to the MetUMN48 resolution. We refer to this resolution as “N48”. We



N96 EQ region N216 EQ region

N512 EQ region N512 WP region

N1024p WP region N1024e WP region

(a) (b)

(c) (d)

(e) (f)

Equator) Equator)

Equator) Equator)

Equator) Equator)

Figure 3. For each model and using time step precipitation on the native horizontal grid, filled boxes and numbers show the lagged cor-relations between the central grid box in each 7× 7 sub-region and grid boxes within each range of distance on the horizontal axis (inunits of the longitudinal grid spacing at the equator, 1x) away from the central point, averaged over all 7× 7 regions. “Centre” denotes theauto-correlation at the central grid box.



TRMM EQ region CMORPH EQ region CMORPH WP region

N96 EQ region N216 EQ region N512 EQ region

N512 WP region N1024p WP region N1024e WP region

j. CMORPH@N96 EQ region k. CMORPH@N216 EQ region l. CMORPH@N512 EQ region

(a) (b) (c)

(d) (e)

(g) (h) (i)

(f)

Figure 4. As in Fig. 2, but using 3 h mean rain rates instead of time step rain rates, retaining the native horizontal grids. Panels (a–c) show3-hourly CMORPH and TRMM data for JJAS 2005, using their native grids. CMORPH is shown for both EQ and WP to demonstrate thesimilarity between the regions. Panels (j–l) show CMORPH averaged to the N96, N216 and N512 MetUM resolutions, respectively, over theEQ region, to compare with panels (d–f).



Figure 5. As in Fig. 2, but using time step rain rates that were first spatially averaged to a 3.75◦× 2.5◦ horizontal grid (MetUM N48resolution).

use N48 to ensure that all models are subject to some de-gree of spatial averaging, following Klingaman et al. (2017).Table 2 shows the number of native-resolution grid boxesin each 3.75◦× 2.5◦ region for each model. Spatial averag-ing reduces temporal intermittency in precipitation at all res-olutions, whether with parametrized or explicit convection(cf. Fig. 5 with Fig. 2). All configurations produce higherprobabilities on the central diagonal and lower probabilitieson the horizontal and vertical axes. The reductions in inter-mittency are greatest for the finest-resolution configurations,with N512 (Fig. 5c) showing much more persistent precipita-tion than N96 (Fig. 5a) over the EQ region. This is due to themuch greater number of N512 grid boxes (113 boxes) aver-aged together to create each N48 grid box, compared withN96 (4 boxes). Applying 2× 2 spatial averaging to N512yielded a highly similar 2-D PDF as in the N96 simulationaveraged to N48 (not shown). Even at N48 resolution, when450 boxes are averaged together, the precipitation from theN1024e configuration (Fig. 5f) remains more persistent thanthat from the N1024p configuration (Fig. 5e), with far fewerprecipitating grid boxes.

3.4 Effects of temporal and spatial averaging

In a similar manner to the results of Klingaman et al. (2017),we find that applying temporal and spatial averaging to 3 h

and ∼400 km resolution, respectively, leads to similar 2-DPDFs for all resolutions of this MetUM configuration thathave parametrized convection, and that these are all too per-sistent relative to TRMM and CMORPH at the same resolu-tions (Fig. 6). The rain-rate PDFs are also remarkably simi-lar between the resolutions, except for slightly more frequentheavy rainfall (and fewer near-zero values) at finer resolu-tions. In contrast, following temporal and spatial averaging,the configuration with explicit convection strongly resem-bles CMORPH and TRMM in temporal persistence and rain-rate PDF, except for having more near-zero values and fewerheavy-rain values. This is discussed further in Sect. 4.3.

3.5 Correlations with physical distance and time

To summarize the spatial and temporal coherence of gridbox, time step precipitation in the model configurations, aswell as the effects of spatial and temporal averaging on thatcoherence, we present correlations of precipitation as func-tions of physical distance (in kilometres) and time (in min-utes). These diagnostics allow the model results to be com-pared more easily than in Fig. 6, because they show correla-tions as functions both of the number of model grid boxes ortime steps and of physical distance and time.

To compute correlations as a function of physical distance,we divide the EQ and WP domains into equal-area regions,



Figure 6. As in Fig. 2, but using 3 h mean rain rates interpolated the 3.75◦× 2.5◦ grid (MetUM N48 horizontal resolution).

then correlate the rainfall in each grid box in each regionagainst the central grid box in the region; correlation valuesare binned by the distance from the central grid box, witha bin width equal to 1x (see Klingaman et al., 2017, for de-tails). In the EQ region, we use 1700 km×1700 km regions sothat the region is at least 41x wide at the coarsest resolutionconsidered (N48). In the WP region, we use 600 km×600 kmregions for native-resolution data, due to the limited size ofthe region, but 1700 km×1700 km regions for N48 data forthe reasons discussed above. Table 2 gives the number anddimensions of the equal-area regions for each MetUM-GA6resolution in each region, including the N48-averaged data,as well as for TRMM and CMORPH.

Correlations with distance show that all configurationswith parametrized convection produce similar spatial scalesof time step precipitation, regardless of resolution, whereas

the N1024e configuration produces very fine-scale features(Fig. 7a). In combination with the 2-D histograms of timestep precipitation in Fig. 2, Fig. 7a emphasizes that refininghorizontal resolution does not fundamentally alter the natureof parametrized convection in the MetUM. Averaging timestep precipitation in either space (to N48; Fig. 7b) or time(to 3 h means; Fig. 7c) increases the spatial coherence ofprecipitation, particularly for the finer-resolution models inwhich more grid boxes or time steps are averaged together.For 3 h mean rain rates, the MetUM-GA6 configurations withparametrized convection produce broader precipitation fea-tures than either TRMM or CMORPH in both the EQ andWP regions, whereas the configuration with explicit con-vection shows much smaller-scale features than the satelliteanalyses.



Figure 7. (a–d) A measure of the spatial scale of precipitation, computed by dividing the domain into equal-area regions and calculating thelag-0 correlations between the central grid box and grid boxes within each distance bin (which are1x wide, starting from 0.51x) away fromthe central grid box, then averaging correlations over all regions in the domain, using (a) time step rain rates on the model configurations’native horizontal grids, (b) time step rain rates averaged to the N48 horizontal grid, (c) 3-hourly rain rates on the native horizontal grid and(d) 3-hourly rain rates on the N48 horizontal grid; (e, f) a measure of the temporal scale of precipitation, computed as the auto-correlation ofprecipitation, averaged over all boxes in the domain, using (e) time step rain rates on the models’ native horizontal grids and (f) time step rainrates on the N48 horizontal grid. The horizontal lines in (a–d) show the range of distances spanned by each distance bin; the filled circle isplaced at the median distance. For clarity, we omit the correlations for zero distance and zero lag, which are 1.0 by definition. In the legends,“-EQ” refers to the EQ analysis domain and “-WP” to the WP analysis domain; “@N48” refers to data averaged to the N48 horizontal grid.



Table 3. Summary metrics of spatial and temporal coherence in precipitation using time step and 3 h data on the native horizontal gridand averaged to the N48 (3.75◦× 2.5◦) grid. Positive values indicate that coherence is more common than intermittency. Higher positive(negative) magnitudes indicate stronger coherence (intermittency). The time step column is marked “n/a” for TRMM and CMORPH becausethese datasets exist only as 3 h values.

Spatial coherence Temporal coherence

Native grid N48 grid Native grid N48 grid

Dataset Region Time step 3 h Time step 3 h Time step 3 h Time step 3 h

N96 EQ 0.27 0.58 0.32 0.41 −0.01 0.68 0.32 0.74N216 EQ 0.29 0.65 0.39 0.44 −0.09 0.74 0.62 0.75N512 EQ 0.33 0.83 0.42 0.44 −0.03 0.60 0.80 0.75N512 WP 0.27 0.86 0.42 0.45 −0.15 0.63 0.78 0.78N1024p WP 0.28 0.92 0.34 0.35 −0.11 0.61 0.89 0.79N1024e WP 0.68 0.72 0.16 0.17 0.91 0.38 0.98 0.63TRMM EQ n/a 0.72 n/a 0.34 n/a 0.33 n/a 0.58CMORPH EQ n/a 0.76 n/a 0.37 n/a 0.43 n/a 0.66CMORPH WP n/a 0.80 n/a 0.42 n/a 0.45 n/a 0.69

Correlations with time show that all configurations withparametrized convection show a strong lag-1 decrease in theauto-correlation of time step precipitation (Fig. 7e), whichpersists even when spatial averaging is applied (Fig. 7f), al-though it reduces in magnitude as more grid boxes are av-eraged together in the finer-resolution models. This furtherdemonstrates the intermittent nature of parametrized convec-tion in MetUM-GA6, which is insensitive to horizontal reso-lution. The N1024e configuration produces a smooth auto-correlation function for time step data, which asymptotesto the same value as the N1024p configuration within the3 h window considered. While the two configurations havesimilar temporal coherence of precipitation at a 3 h lag, theN1024p configuration achieves this by averaging intermit-tent time step convection, whereas the N1024e configura-tion achieves this by averaging persistent convective eventsof various lifetimes ranging from a few time steps to severalhours.

3.6 Summary metrics

Table 3 presents summary metrics from ASoP1 of the spa-tial and temporal coherence in precipitation using time stepand 3 h data on the native horizontal grids and averagedto the N48 grid. These metrics are computed from the co-herence of upper-quartile and lower-quartile precipitation inspace and time; higher positive values indicate greater co-herence. The metrics reflect the findings above. All modelswith parametrized convection show temporal intermittencyin time step data on the native grid, regardless of modelresolution; spatial coherence is also low. After averaging to3 h scales on the models’ native grids, there is a large in-crease in temporal and spatial coherence of tropical rain-fall in all model simulations with parametrized convection.In this case, there is a noticeable increase in spatial coher-

ence as model resolution increases (reflecting the decreasinggrid size, since the metrics are computed on the native grid),while there remains no systematic change in temporal coher-ence with resolution. The spatial coherence at this timescaleis similar to that in the satellite-derived datasets, while thetemporal coherence is noticeably greater.

Both the satellite-derived rainfall datasets and the modelsimulations show a reduction in spatial coherence of tropicalrainfall at the 3 h timescale following averaging to the coarserN48 resolution, while the temporal coherence increases. Thereduction in spatial coherence at N48 relative to the nativegrids occurs because the metrics are computed based on afixed distance in gridpoints (of the input data), rather than afixed physical distance; a coarser grid would be expected tohave less coherent precipitation, due to the greater physicaldistance between gridpoints. On the N48 scale there is a moresystematic increase in temporal coherence at finer model res-olutions, particularly for the time step data (partly, at least,due to the decreasing time step with increasing model reso-lution). Overall, the values show that, following spatial andtemporal averaging, the simulations with parametrized con-vection show only slightly larger spatial and temporal coher-ence than the satellite-derived rainfall, and little systematicchange in either temporal or spatial coherence with resolu-tion.

The metrics also illustrate the contrasting behaviour of theN1024e configuration. This shows high temporal and spatialcoherence at the time step, gridscale level (consistent withFig. 3f), which suggested persistent rainfall isolated to oneor two grid boxes in this configuration. Spatial coherence re-mains similar upon temporal averaging but decreases sharplyupon spatial averaging, due to the isolated nature of explicitconvection at this grid size. The temporal coherence of thetime step data remains high following spatial averaging butdecreases upon temporal averaging (suggesting the events



rarely last for longer than 3 h and are followed by prolongeddry intervals).

Ultimately, following averaging to the N48 grid and 3 hscale, the temporal and spatial coherence of tropical rain-fall from all the model simulations is similar to that fromthe satellite-derived datasets.

4 Spectral characteristics

To examine the distribution of precipitation intensity on arange of spatial and temporal scales, and its sensitivity totemporal and spatial averaging, we compute the contribu-tions of discrete bins of precipitation intensity to the totalprecipitation at a grid box. The result is a spectrum thatshows the relative importance of precipitation events in agiven intensity bin to the total precipitation. As in Klinga-man et al. (2017), we use 100 bins of varying width, definedby the following equation and sampling rainfall intensities inthe range of 0.005–2360 mm day−1:

bi = e

ln(0.005)+[i·(ln(120)−ln(0.005))2

59

] 12

, (1)

where i is the number of the bin and ranges from 1 to 100,and ln(x) is the natural logarithm of x. A further lower binedge is added at 0.0 to ensure that a histogram of countscomputed using these bins sums to the number of valid datapoints in the sample. By calculating these contributions atmany grid boxes in a region, we produce maps of the con-tributions of various precipitation intensity bins to the totalprecipitation at each grid box (e.g. Fig. 8). Regional averagesof the spectra can also be produced for direct comparison be-tween datasets, although it should be noted that this processintroduces a spatial averaging of the spectra themselves andhence is best done for relatively small regions only.

Analysis of the spectral characteristics of these runs pro-vides further evidence of the points made in Sect. 3, and al-lows us to investigate the influence on rainfall amounts atlonger timescales. They also illustrate the effects of tempo-ral and/or spatial averaging of time step/grid-box data, whichcan indicate temporal and spatial intermittency. We analysethe spectral characteristics on each given timescale at eachgrid box of the dataset (at whichever resolution is being anal-ysed). We then use spectra averaged over particular regions toillustrate the characteristics of this model configuration. Theregions were chosen based on typical climatological bias re-gions illustrated in Walters et al. (2016): wet bias regions ofthe equatorial Indian Ocean, southern China and the westernPacific, and the western Africa dry bias region.

4.1 Influence of resolution

We first compare the rainfall spectra at the native grid andtime step among model resolutions. Noting that the time steplength is shorter at the higher horizontal resolutions (see Ta-ble 1), the broad similarity, particularly over the ocean, be-tween the spectral maps at native resolution, even as the hor-izontal resolution is increased 5-fold, is remarkable (Fig. 8)and suggests that the convection parametrization behaviourin the tropics is not very scale aware (except perhaps forlarger rainfall events). Closer examination of the spectra indifferent regions (Fig. 9a and b, solid lines) reveals that thehigher-resolution simulations do, as expected, produce morefrequent, higher intensity time step events on the native grid,particularly for the land region of western Africa (WA do-main; Fig. 9b). However, when the higher resolutions are allaveraged to N48 (Fig. 9a and b, dashed lines), the rainfallspectra are shifted to smaller intensities in all cases and thedifferences in the tail of the distribution are no longer appar-ent, suggesting that those events were spatially isolated. Wealso note that the effects of spatial averaging are larger forthe higher model resolutions in which more grid boxes areincluded in the average. This illustrates the spatial intermit-tency that was highlighted in Sect. 3. However, the largestimpact of spatial averaging is seen for the N1024e configu-ration. This is discussed further in Sect. 4.3.

When the precipitation data are all averaged to the N48grid and 3 h timescale (in a similar manner to Sect. 3.4),Fig. 9c–f show that the models all tend to underestimatethe 3-hourly rainfall amounts compared with TRMM andCMORPH, and that increasing the horizontal resolution doesnot improve the comparison on this timescale for tropicalrainfall over the ocean. Indeed, we see little evidence thatincreasing the horizontal resolution has any overall effecton the rainfall distribution over ocean on these scales in thesimulations with parametrized convection. Over the westernAfrican land region, the higher-resolution configurations doshow an increase in the fractional contribution from higher3 h totals and a corresponding decrease in the lower amounts,but this is not apparent over southern China. We note that thelargest change in the spectral characteristics is seen when theconvection parametrization is switched off. This is discussedfurther in Sect. 4.3.

4.2 Looking across timescales

We next examine how the spread of rainfall amounts changesas the data are averaged to successively longer timescales.We continue to examine the datasets once averaged to theN48 grid in order both to compare spectra at the same ef-fective resolution and to ensure that at least some horizon-tal averaging has been done on all datasets. Data from theN96, N216 and N512 simulations, for June–September in-clusive, are averaged to 3-hourly, daily, 10-day and 20-daytimescales, over the years shown in Table 1. CMORPH data



Figure 8. Spectral maps of time step precipitation in JJAS from three MetUM GA6 configurations: (a) N96, (b) N216 and (c) N512. Dataare analysed on each configuration’s native grid. For each panel, the fractional contributions from all bins within the given intensity rangeare summed at each grid box. Time step lengths and years analysed are shown in Table 1.

are also used for comparison, using the years mentioned inSect. 2. Two oceanic regions and two land regions are se-lected in order to highlight the main findings.

The movement of the spectra towards smaller values whenaveraged to successively longer timescales indicates thatthere is variability at the longer timescale (such that includingdrier periods in the average decreases the longer timescalemean). For all of the regions shown in Fig. 10, the pro-gressive shift of the spectra from CMORPH towards smallervalues as the timescale is increased from 3 h to 20 daysis not matched by the model results, which tend to showless movement and therefore lack variability on the longertimescales. This is particularly noticeable for tropical rain-fall over the oceans; for the two regions shown in Fig. 10aand c the N96 configuration underestimates the rainfall to-tals at shorter timescales but overestimates them at longertimescales. The spectra of daily mean values agree reason-ably well with those from CMORPH, but the model lacksvariations on timescales of ∼10 days so that the spectra forthe 10-day and 20-day means peak at larger values in themodel than in CMORPH. This is confirmed in Fig. 11a and cwhere auto-correlations of daily rainfall with increasing timelag for these regions are consistently higher in the model

than in the satellite rainfall datasets. For southern China,the daily rainfall spectrum tends towards large values, sug-gesting a lack of sub-daily variability, while the day-to-dayvariability is in reasonable agreement with the observations(Fig. 11d). All three of these regions exhibit positive rain-fall biases in the MetUM-GA6 configuration’s climatology(Walters et al., 2016). In contrast, the western African region(Fig. 10b) shows spectra on all timescales that are displacedto smaller rainfall totals than CMORPH, consistent with aclimatological dry bias. For this region, there is disagreementon the day-to-day variability between the two satellite-basedrainfall estimates, with TRMM suggesting more persistence(higher autocorrelations) than either CMORPH or the model.These differing characteristics between the two measures ofactual rainfall amounts are likely related to their differentsatellite data sources and the algorithms used to combinethose sources. It is known that both datasets tend to underesti-mate smaller daily rainfall totals and can overestimate largerones (e.g. Tian et al., 2010), but details on the day-to-dayvariability of rainfall in these two datasets are lacking in theliterature. Thus, we cannot make a definitive statement aboutthe validity of the characteristics of daily rainfall variations



Figure 9. (a, b) Precipitation spectra averaged over different regions for the five model configurations. Solid lines show spectra at nativeresolution and time step while dashed lines show the spectra from each configuration when precipitation data are averaged to the N48 grid:(a) “WP” domain; (b) “WA” domain. (c–f) Precipitation spectra averaged to the N48 grid and 3 h timescale, for (c) “WP” domain, (d) “WA”domain, (e) equatorial Indian Ocean (60–80◦ E, 10◦ S–5◦ N), (f) southern China (103–119◦ E, 23–32◦ N). N1024 data are not available forthe latter two regions. Also included in each panel are results from the CMORPH and TRMM satellite-based rainfall analyses averaged tothe same spatial and temporal scale.

in the models compared with satellite-based estimates overthe western African region.

Figures 11 and 12 show the same comparison but for theN512 configuration. As indicated in Sect. 4.1, this 5-fold in-crease in horizontal resolution has little consistent impact onthese characteristics of tropical rainfall variability. Compar-ison across these timescales of spectra derived from thesetwo configurations at their native resolutions, compared withCMORPH data averaged to each of those model grids (notshown), indicates a similar lack of consistent improvementat the higher resolution.

4.3 Explicit vs. parametrized convection

The results presented above suggest that, generally, MetUM-GA6 configurations with the deep convection parametriza-tion switched on have similar spectral characteristics acrosstimescales despite differing grid sizes and time steps. Onlyonce the deep convection scheme is switched off do the char-acteristics change markedly. The N1024e simulation with ex-plicit convection produces extremely high intensity time stepevents, which persist for up to 3 h (Fig. 3f). Thus, in contrastwith the N1024p simulation, there is virtually no differencebetween the spectra from the N1024e time step data and 3 haverages on the native grid (light and dark green curves onFig. 13a and c), showing limited effects of temporal averag-ing. However, as illustrated in Fig. 3f and Fig. 7a, the high-



Figure 10. Spectra of 3-hourly, daily, 10-day and 20-day rainfall totals (in mm day−1) from the MetUM-GA6 N96 configuration (solid lines),averaged over four regions: (a) “WP” domain; (b) “WA” domain, (c) equatorial Indian Ocean (10◦ S–5◦ N, 60–80◦ E) and (d) southern China(23–32◦ N, 103–119◦ E). Corresponding spectra from CMORPH are shown by the dashed lines. Rainfall data were first averaged to the N48grid in both cases.

intensity time step events are isolated to only one or two gridboxes any given time, so spatial averaging has a large impact(cf. the pairs of green and purple lines in Fig. 13a and c).Further, once spatial averaging has been carried out, the sub-sequent effects of temporal averaging between time step and3 h scales are negligible (the light purple curves in Fig. 13aand c are almost hidden by the dark purple curves). In con-trast, for N1024p (see Fig. 13b, d) there are effects from bothtemporal and spatial averaging of the time step data becausethey are both temporally and spatially intermittent. However,once again, following spatial averaging of the time step datato∼400 km scales, the subsequent effects of averaging to 3 hscales are negligible.

In both cases, the spatially averaged spectra of fractionalcontributions to 3-hourly rainfall peak at lower intensitiesthan the satellite rainfall datasets. In N1024p, both spatialand temporal intermittency contribute to this underestimate.In N1024e, even the excessive rainfall amounts in isolatedgrid boxes are not sufficient to compensate for the largenumber of surrounding grid boxes with no rainfall. How-ever, for the WA region, the N1024e simulation does appearto represent the distribution of 3-hourly rainfall rather bet-ter than N1024p. In configurations with parametrized con-vection, some of the underestimate in the 3 h totals over the

land regions is related to the poor diurnal cycle of rainfall(see, e.g., Stratton and Stirling, 2012; Kendon et al., 2012),whereby deep convection starts and ends too early in theday and rainfall amounts in the evening and overnight areunderestimated. The configuration with explicit convection,in common with other convection-permitting configurations(e.g. Hohenegger et al., 2008), has improved timing of thisdiurnal cycle (not shown), partly due to the unrealistic sizeof the grid boxes used, which delay the start of deep convec-tion but results in rainfall amounts that, once started, are verylarge and persist for a few hours. Similar analysis of a 4.5 kmresolution MetUM configuration with explicit convectionover Africa also shows an improved diurnal cycle of convec-tion over land, but suggests that the extreme spatial intermit-tency is reduced as the grid size decreases, and that the over-all rainfall bias is smaller (R. Stratton, personal communica-tion, 2016). Thus, our analysis demonstrates that the ASoP1methods are able to identify contrasting behaviour of rain-fall variability between simulations with parametrized andexplicit convection. As noted previously, the grid size usedfor this experiment is clearly unrealistic for explicit convec-tion. Indeed, the use of a N1024 resolution for parametrizedconvection may also be questionable (Molinari and Dudek,1992). Future work using these methods will investigate how



Figure 11. Auto-correlations of precipitation at different time lags, computed using daily precipitation on the N48 horizontal grid, averagedover the four regions shown in Fig. 10.

these characteristics change as resolution is increased furthertowards the ∼100 m scale.

5 Discussion and conclusions

In order to have confidence in climate model projections ofprecipitation, it must be demonstrated that the modelled rain-fall responds appropriately to changing atmospheric condi-tions on all scales. The ASoP1 methods designed by Klinga-man et al. (2017) provided an additional tool for comparingand evaluating simulated rainfall variability between modelconfigurations and with various observational datasets. Anal-ysis of the spatial and temporal characteristics of rainfall in aset of parallel configurations of the MetUM-GA6 model us-ing the ASoP1 methods has allowed several characteristics oftropical convection in these model configurations to be iden-tified:

1. Precipitation produced by the convection parametriza-tion on the native grid and time step in MetUM-GA6 is

both spatially and temporally intermittent, regardless ofthe horizontal resolution and time step of the model, atleast for the broad range of resolutions (20–200 km) andtime steps (5–20 min) considered here. This behaviouris caused by the choice of closure at GA6, in which themass flux amplitude is set to depend on the CAPE de-tected in the grid box, rather than the rate of atmosphericdestabilization. The resultant heating applied producesan inversion at the top of the boundary layer on the nexttime step that the diagnosis deems too strong to allowconvection to initiate. It remains in this state until theinversion has been eroded by a combination of heatingin the boundary layer, and large-scale ascent. This be-haviour occurs immediately at the start of the simula-tion with no spin-up, regardless of grid size or time steplength. Klingaman et al. (2017) found similar behaviourin 2-day forecasts with an earlier MetUM version.

2. With parametrized convection, the fractional contribu-tions to total precipitation from different intensities on



Figure 12. As Fig. 10 but for the MetUM-GA6 N512 configuration.

Figure 13. Spectra of time step (5 min) and 3-hourly rainfall contributions, at native resolution and averaged to the N48 grid, from (left)MetUM-GA6 N1024e and (right) N1024p configurations, averaged over (top) the “WP” domain and (bottom) the “WA” domain.



the native grid and time step are also largely insensitiveto horizontal resolution and time step in MetUM-GA6.

3. When the convection parametrization is switched off,albeit at an unrealistic resolution for explicit convec-tion to be represented properly, the time step precipi-tation becomes very persistent on scales up to the or-der of a few hours, but even more isolated on the grid-scale, likely due to the considerable dynamical forcingrequired to lift a 20 km × 13 km grid box. Convectiveheating associated with explicit convection sets up sig-nificant ascent in the convecting column, which contin-ues the destabilization of the column, while adjacentcolumns experience descent and so convection is sup-pressed.

4. For MetUM-GA6 configurations with parametrizedconvection, spatial and temporal averaging to scales∼400 km and∼3 h reduces the spatial and temporal in-termittency considerably. At these scales, the convec-tion scheme starts to display sensitivity to the large-scale forcing, as the strength of this is what determinesthe frequency with which the convection scheme canbe activated. However, MetUM-GA6 produces precip-itation features that are too broad relative to the TRMMand CMORPH satellite-derived analyses.

5. For the MetUM-GA6 configuration with explicit con-vection used here, temporal averaging to scales of ∼3 hhas little effect on the rainfall intensities, while spatialaveraging to scales of ∼400 km has a very large effect,due to the large spatial intermittency.

6. Comparison of the model configurations’ tropical pre-cipitation variability on horizontal scales of ∼400 kmand timescales from daily to 20 days (intraseasonal)shows no systematic difference in behaviour betweenthe different resolutions. In all cases, the model tends tounderestimate the amplitude of the intra-seasonal vari-ations (i.e. there are not enough drier days), over theocean, at all resolutions.

7. The lack of intra-seasonal variability contributes to anoverall wet bias in some oceanic regions (e.g. the equa-torial Indian Ocean, the western Pacific and southernChina), while underestimations of rainfall intensity onsub-daily and daily timescales in western Africa are as-sociated with a climatological dry bias.

Attributing climatological biases in regional precipitationto deficiencies in model physical parametrizations remains achallenge for model developers. Such biases can have impli-cations for weather and climate modelling on a wide range oftemporal and spatial scales, from inhibiting moisture trans-port through intra-seasonal propagation of convection (e.g.Bush et al., 2015; Kim et al., 2016) to contributing to uncer-tainty in projections of future tropical rainfall (e.g. Kent et

al., 2015). By examining the behaviour of modelled tropicalrainfall at a wide range of spatial and temporal scales, wecan hope to shed light on the way in which such biases de-velop. Our results suggest that, in many regions, sub-seasonaltropical rainfall in the MetUM-GA6 configuration lacks vari-ability on all but the smallest available temporal and spatialscales (i.e. the model time step and gridscale). This suggestsa lack of response from the convection parametrization tochanging atmospheric conditions. Instead, at the time stepand gridscale, the spatial and temporal intermittency appearsto be quasi-random, much like the MetUM-GA3 configura-tion analysed by Klingaman et al. (2017). Such analysis pro-vides information to model developers, which should help toinform the future direction of parametrization development.

The apparent lack of sensitivity to horizontal resolution is,at first sight, in contrast with other model studies, which sug-gest an improvement in rainfall characteristics as horizontalresolution is increased (e.g. Wehner et al., 2010; Kopparla etal., 2013; Prein et al., 2013; Tripathi and Dominguez, 2013).However, several of these studies compare the results on thenative grid of each model with observations at resolutionsthat are often higher than in any of the model configurations.This will, naturally, highlight the improved representationof the natural spatial variability of rainfall arising from lo-cal dynamical gradients, orography, etc., in higher-resolutionmodels. Indeed, Prein et al. (2013) commented that “Themajor advantages of high-resolution simulations are foundfor small scales” and that, at scales above ∼100 km, theirhigher-resolution runs show only “small advantages” overtheir lower-resolution runs. However, Kopparla et al. (2013)point out that such comparisons differ between regions.

Furthermore, the use of daily mean values in most of thesestudies hides issues with sub-daily variability such as spa-tial and temporal intermittency and a poor diurnal cycle. Weacknowledge that many of the characteristics we highlightin our study may be particular to the MetUM-GA6 configu-ration and its convection parametrization. However, Klinga-man et al. (2017) showed that there are other models, witha wide variety of horizontal resolutions, which also showspatial and intermittency in time step tropical rainfall. Wehope that our results will encourage similar systematic stud-ies of the effects of horizontal resolution in other models.Our finding that the effects of switching off the convectionparametrization and allowing explicit convection, albeit onunrealistic spatial scales, has a much more marked impact onthe tropical rainfall characteristics, motivates further studyon the sensitivity to the convection parametrization itself.A recent study by Jin et al. (2016) suggested that resolu-tion sensitivity in the diurnal cycle of rainfall over Chinasimulated by the Weather Research and Forecasting (WRF)model is strongly related to the increasing contribution fromnon-convective rainfall, while the contribution from con-vective precipitation remains similar unless the convectionparametrization is altered.



Finally, the increasing number of studies using convection-permitting resolutions with grid-lengths of a few kilometres(e.g. Fosser et al., 2015; Kendon et al., 2012; Prein et al.,2013) suggests that, while such models do exhibit improvedsub-daily characteristics and diurnal cycles of rainfall, prob-lems remain with excessive rainfall rates and too persistentprecipitation events at these resolutions. It is clear that simi-lar analyses of tropical rainfall characteristics in convection-permitting models at resolutions <∼1 km would be enlight-ening and of significant use in model development.

6 Code and data availability

The source code for the model used in this study, Me-tUM, is free to use. To apply for a licence for MetUMgo to http://www.metoffice.gov.uk/research/collaboration/um-partnership (Met Office UM Partnership Team, 2016).The availability of the ASoP1 diagnostics package is detailedin Klingaman et al. (2017). MetUM-GA6 model data arearchived at the Met Office, and are currently available to UMpartners. TRMM 3B42 version 7A data can be obtained fromhttp://disc.sci.gsfc.nasa.gov/TRMM (National Aeronauticsand Space Administration, 2016). CMORPH version 1.0data can be obtained from ftp://ftp.cpc.ncep.noaa.gov/precip/global_CMORPH/3-hourly_025deg (National Centers forEnvironmental Prediction Climate Prediction Center, 2016).

Author contributions. N. Klingaman analysed the spatial and tem-poral intermittency and G. Martin and A. Moise analysed the spec-tral characteristics of the rainfall data. G. Martin and N. Klingamanwrote the manuscript with input from A. Moise.

Competing interests. The authors declare that they have no conflictof interest.

Acknowledgements. G. Martin was supported by the Joint UKBEIS/Defra Met Office Hadley Centre Climate Programme(GA01101). N. Klingaman was supported by an IndependentResearch Fellowship from the UK Natural Environment ResearchCouncil (NE/L010976/1). A. Moise was supported by funding fromthe Australian Climate Change Science Program. The authors aregrateful to the model development teams at the Met Office, who ranthe MetUM-GA6 simulations as part of the Global Atmosphere 6.0development process, and to Alison Stirling for helpful commentson the manuscript.

Edited by: S. ArndtReviewed by: two anonymous referees

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